Swedish Institute for Social Research (SOFI) ____________________________________________________________________________________________________________

Stockholm University ________________________________________________________________________ WORKING PAPER 2/2012 MASTERS OF OUR TIME: IMPATIENCE AND SELF-CONTROL IN

HIGH-LEVEL CHESS GAMES

by

Patrik Gränsmark

MASTERS OF OUR TIME: IMPATIENCE AND

SELF-CONTROL IN HIGH-LEVEL CHESS GAMES∗∗∗∗

PATRIK GRÄNSMARK

Abstract

This paper presents empirical findings on gender differences in time preference and inconsistency based on international, high-level chess panel data with a large number of observations, including a control for ability. Due to the time constraint in chess, it is possible to study performance and choices related to time preferences. The results suggest that men play shorter games on average and pay a higher price to end the game sooner. They also perform worse in shorter game compared to women but better in longer games. Furthermore, women perform worse in time pressure (the 40th move time control). The results are consistent with the interpretation that men are more impatient (with a lower discount factor) but also more inconsistent in the sense that they tend to be too impatient. Women, on the other hand, are more inconsistent as they tend to over-consume reflection time in the beginning, leading to time pressure later.

Keywords: Time preference, time inconsistency, impatience, gender, self-control problems

Classification codes: J16, D03, D91

∗ I am grateful for the comments by Christer Gerdes, Magnus Johannesson, Åsa Rosén, Anders Stenberg, Eskil Wadensjö, Robert Östling, the participants at the SOFI seminar and the anonymous referees. I also thank ChessBase and the 1,620 chess players participating in the survey.

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1. Introduction

We have all experienced moments of regret at leaving unpleasant tasks for later although we

know we would be better off in the long run by doing them now. This is also true for pleasant

tasks, or rewards, which we tend to carry out, or consume, earlier than we would prefer in the

long run. Such acts are said to be due to self-control problems as we are just too tempted by

the present utility to care sufficiently about the long-term utility. We also know that people

differ in degrees of impatience as some people seem to be able to wait patiently for a higher

reward while others want instant action although it will result in a lower payoff. Contrary to

the concept of time preferences (impatience), time inconsistency (self-control problems)

distinguishes between short- and long-term values. Angeletos et al. (2001) give a neat

example. When we go to bed at night most of us set the alarm to wake us up at a certain time.

Nevertheless, when the alarm sounds some of us just hit the snooze button, pull up the duvet

and go back to sleep. We then tend to hit the snooze button repeatedly until we have to skip

the healthy breakfast, have a swift cup of coffee and lock the door at the same time as we put

our coat on. In this case, we consume too much time to the point where we experience

subjective discomfort in the shape of stress. Such behavior is time inconsistent as our long-

term preferences are not consistent with our short-term preferences. However, if we intended

to snooze for a while before getting up then the behavior is time consistent as our preference

did not change during the night. In practice, it may be difficult to observe whether there was

an intention to snooze or not, which may be one explanation as to why there are so few

empirical studies on time inconsistency.

The purpose of this paper is to examine potential gender differences in time preferences

and time inconsistency by using an extensive panel dataset from international high-level chess

games. Due to the time restriction in chess, a player can consume or save time for each move,

where the move quality is a function of the time spent on that move. I investigate how eager

women and men are to end the game although it implies a cost, how they perform in games

shorter and longer than average, and also to what extent women and men end up in time

pressure (approximated by performance at the 40th move time control, see section 2.4). I

complement the data with unique survey data, collected at the world´s leading chess site,

www.chessbase.com. In the survey, 235 expert chess players, with data from 18,000 games

available, were asked to answer questions (rating answers from zero to ten) about impatience,

performance under time pressure, risk taking and smoking habits (smoking is considered to be

a typical self-control problem). The findings reveal that men are more impatient than women

on average as they play shorter games and are willing to pay a higher price for ending the

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game earlier. Combined with the results of the survey, the findings suggest that both male and

female players are time inconsistent but in different directions. Male players tend to be too

impatient as they play too fast in the beginning of the game, while female players tend to

over-consume reflection time in the beginning, leading to time pressure when approaching the

40th move time control. The fact that the survey consists of self-reported data suggests that the

players are indeed aware of the inconsistency. The survey also shows that time preferences in

chess are positively correlated with time preferences in real life, which strengthens the

external validity of the findings. In addition, smokers are more impatient on average but are

likely to be inconsistently impatient (as smoking is positively correlated with being too

impatient).

Akerlof (1991) writes that time inconsistency could contribute to “poverty of the elderly

due to inadequate savings for retirement, addiction to alcohol and drugs, criminal and gang

activity, and the impact of corporate culture on firm performance.” If one of the sexes is more

impatient or time inconsistent than the other then consumption and savings could differ

substantially during a lifetime.1 With their empirical paper, Ashraf et al. (2006) showed that

saving behavior can indeed be affected by time inconsistency. In detail, they find that women

are, or at least consider themselves to be, more time inconsistent when studying savings

among bank clients in the Philippines. The research results on time preference and gender

diverge somewhat although there is some indication of male students being more impatient

than female students. However, in an influential paper by Harison et al. (2002), no gender

difference in discount factor was found when looking at a more representative (general)

sample.

In experimental studies addressing discounting over time, it is common to include

money as a means of measuring the degree of impatience. When doing so it is important to

control for wealth, as a potential gender difference in impatience could otherwise be due to

the fact that differences in wealth can lead to a different valuation of money. The time frame

must typically be rather large as it would be difficult for most people to perceive a difference

from one day to another. In a practical experiment $100 now is the same for most people as

$100 a few hours later (the problem of just perceptible differences). For this reason, the

1 In his theoretical paper, Strotz (1956) was the first researcher to suggest that people are more impatient in the short run than in the long run. Pollack (1968) and Phelps and Pollack (1968) gave an early formal model of time inconsistency which has later been extended and refined by Akerlof (1991), Laibson (1997), O´Donoghue and Rabin (1999), and Fischer (1999). For another paper on time inconsistency, see Ariely and Wertenbroch (2002). See also DellaVigna and Paserman (2005) for an empirical work on time preferences, Benzion et al. (2004) on time inconsistency and Croson and Gneezy (2009) for an overview of gender differences in economic preferences.

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experiments are abstract, i.e., the participants are supposed to imagine an abstract time period

of, for instance, one year. If the experiments were to last for a whole year it would be

impossible to control for changing factors in the lives of the participants as they could not be

isolated from the world for a year. In a chess game, that usually lasts for a few hours, no

money is involved so any effect of wealth should be diminutive.2 As a corollary, there is no

need to study agents for a longer time period. The longer the time frame in an experiment, the

higher the risk that external conditions will change, with obscure impact to follow.

Consequently, when using chess data we do not have to worry about wealth, remaining

lifetime or different perceptions of the interest rate when measuring discounting over time.

The most obvious advantage with chess data, however, is the existence of the Elo rating

which very accurately approximates the chess ability of a player on a metric scale. Moreover,

the difference in Elo ratings between two players corresponds to a certain probability that a

player will defeat the opponent.3 This is further explained in section 2.

Why should economists bother to study high-level chess players? A frequently

employed assumption in economics is the assumption of full rationality. However, most

economists probably agree that full rationality is not very realistic and to obtain an image of

how close we can expect people to be, it is important to study highly rational and competitive

subgroups such as expert chess players. High-level chess players have been studied numerous

times for this reason, for instance by Levitt et al. (2009) and Palacios-Huerta and Volij (2009)

who focus on expert chess players in a lab experiment to investigate whether it is reasonable

to test backward induction through the centipede game. Furthermore, compared to sports

economics, chess has the advantage that different groups can be compared more easily as

there is no requirement of physical strength. Indeed, chess is one of the few competitive

events where men and women enter in direct competition.4 Moreover, the rules in chess are

globally homogenous which facilitates comparisons further.

This paper contributes to the literature by presenting empirical findings on two

traditional economic topics, impatience and self-control problems, where focus is set on

gender differences. Gender differences in time preferences and inconsistency have only been

studied in a handful of papers and a consensus is still lacking. With the unexplored data used

here together with the survey data, I am able to treat the topic from a new perspective. 2 The prize money in chess levels below the absolute world elite can be ignored as it is too small to be important in this context. 3 For a second opinion on the qualities of the Elo ratings, see Moul and Nye (2009, p. 11) and Chabris and Glickman (2006, p. 1040)). For other studies of chess players, see Gobet (2005), Ross (2006) and Roring (2008). See also van Hareveld et al. (2007) for a study on time pressure in chess. 4 For a discussion about women’s situation in the chess world, see Shahade (2005).

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The paper is organized as follows. The next section provides a theoretical background

while section 3 discusses the data and statistics. Section 4 presents the results of the

estimations and section 5 concludes.

2. Conceptual framework

2.1 Risk-taking in chess

In many games and sports there are only two outcomes: a win or a loss. In chess, however,

there is also a third outcome: a draw (a tie). A win gives one point, a draw half a point and a

loss zero points. Particularly interesting from a risk perspective, is that a draw can be offered

and either accepted or rejected at any point of the game. These aspects make chess very

suitable for the study of risk taking behavior. A risk-averse player will have a higher

preference for a draw since it gives half a point with certainty rather than gambling by playing

for a win or a loss. A risk-loving player will prefer to play for a win with the risk of losing.

Expressed differently, a risk-averse player faces a concave utility function while a risk-loving

player has a convex utility function.

The so called chess openings (the initial development schemes for the chess pieces)

have been extremely well analyzed for more than a century. From analyses and real game

history, probabilities of certain outcomes for certain openings are well known, i.e., the

likelihood that a game ends in a win, draw and loss. This is easily demonstrated with an

example: Suppose two equally good opening categories, A and B, have different probabilities

of resulting in a draw. Opening A leads to a win in 40 percent of the cases, a loss in 40

percent, and a draw in 20 percent. Opening B leads to a win in 30 percent of the cases, a loss

in 30 percent, and a draw in 40 percent. A risk-averse player will have a preference for

opening B whereas a risk-loving player will have a preference for opening A.

All major opening categories have been classified into the so called ECO code system,

consisting of 500 main categories. The database contains information about what ECO code

was played in each game and by using the classification developed by Gerdes and Gränsmark

(2010), I am able to control for the level of risk taking in each game and for each player.5

5 The risk classification in Gerdes and Gränsmark (2010), was constructed by carrying out a survey among eight chess experts (with an Elo ranging from 2000 to 2600, three women and five men). They were asked to label each ECO code (from both white´s and black´s perspectives) as being either risky, neutral or risk-averse. Six out of eight experts had to agree to classify an opening code as being either risky or risk-loving, otherwise, it was denoted as neutral. Intuitively, the most straight-forward way to construct such a measure would be to just employ the outcomes of the games, however, such a measure would only supply one risk indicator per game. In addition, by studying the opening phase we get a clear indication of the actual intention that each player had in

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When employing the survey data, I also include a self-reported risk measure, see section 3.

We cannot be sure to what extent these risk indicators capture the true risk preferences.

However, the results in Table 4 are the opposite to those expected had the gender difference

been driven by risk preferences.

2.2 The Elo rating

An advantage with chess data is the existence of the Elo rating system, named after its creator

Arpad Elo (1978). In this study only players with at least 2000 in Elo rating are included (with

the maximum rating being the world record of 2851). When players win a game, they increase

their Elo rating while the Elo rating of the defeated player decreases. An inferior player who

wins a game wins more Elo points than a superior player. The difference in Elo between two

players corresponds to an exact expected scoring probability and, since all Elo ratings are

common knowledge, the expected score is known in advance. For instance, if a player has an

Elo rating of 2300 and the opponent of 2100, the superiority measured in Elo difference is

200. This corresponds to an expected score, ( )1,0∈ϕ , of .75. If the players are equally skilled,

i.e. the Elo difference is zero, the expected score is .5.6 By controlling for the Elo rating and

the Elo difference in the econometric estimations, it is possible to reduce a potential bias

occurring due to the fact that men and women may have different chess abilities.7 By having

information about the expected score in a certain game, it is possible to compare the

performance in the game in focus with the expected score. I will take advantage of this as

accepting a draw when being superior (i.e., 5.>ϕ ) means that the player is willing to pay a

price for achieving the draw in the present. As both the result (a draw) and the expected score

are available in the data, it is possible to calculate a potential gender difference in the cost

men and women are willing to accept.

the beginning of the game, which is not confounded by aspects occurring during the course of the game. Since it is not clear how the game outcome is affected when two extremes meet, it is preferable to have one risk indicator for each player, which was the motivation behind the expert survey. However, the two risk measures are positively and significantly correlated. 6 In chess the player of the white pieces starts the game and has a first-mover advantage. I disregard that fact here for reasons of simplicity. However, since the color of the pieces is random (decided by a lottery before the 1st game in the event), there is no loss of generality. 7 To see the usefulness of such a measure, we can compare it to the controls included in studies on gender wage gap comparisons where the researchers want to hold constant for gender differences in education, IQ and experience.

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2.3 Impatience in chess

The quality of a chess move depends positively on the time of reflection allocated to that

move, with decreasing returns. The quality of move t is the short-term utility of period t while

the game quality (performance, i.e., a win, a loss or a draw) is the long-term utility. The

available time is restricted and to maximize the long-term utility, the player wants to find the

optimal allocation of time for each move. An impatient player prefers shorter games although

this means performing worse. The time constraint in standard international chess implies that

each player has a maximum of two hours for the first 40 moves and then an additional 60 or

90 minutes for the remainder of the game.8 Under these conditions the maximum duration of a

game would be six to seven hours. The two hours can be distributed among the 40 moves in

the way the player wishes. Just as in exponential discounting, one can choose to consume or

save time for each move. Time is the good that can be consumed or saved and each chess

move represents a time period. It is possible to consume less time in the beginning of the

game which can be used later in the game. If fewer than 40 moves have been played when the

two hours end, the game is lost. Hypothetically, there may be players that over-consume

reflection time in the beginning of the game but also players who, due to inconsistent

impatience, under-consume reflection time. The former group is more likely to have to play

under time pressure than the average player while the latter group is more likely to have to

play under time pressure less than the average player. In the case of under-consumption of

time, a player fails to reach the optimal move quality. Thus, both under- and over-

consumption is an inconsistent behavior. However, a player may deliberately choose a

suboptimal allocation (measured in mere score points) if the long-term utility is increased, i.e.,

a player can discount over time.

The typical question used in lab experiments when studying time preferences is ”Do

you prefer $100 today or $110 a year from now?” By varying the amount and the time

periods, it is possible to obtain a function and a discount factor. Implicitly, chess players have

to ask themselves a similar question every time they are to move. They have to decide

whether they prefer half a point (a draw) now or the expected score later in the game. If a

superior player faces an expected score of .6, she has to ask herself whether she prefers .5

now to .6 later. Since .6 is the expected score, she doesn’t know with certainty that she will

have .6 later but given that we can remove the effect arising from risk preferences, this is the

same questions as the one asked in the lab. Theoretically, to net out a potential risk taking

8 A chess clock contains two clocks, one for each player.

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effect from the impatience effect, we need to know that EU(.6) equals or exceeds U(.6).

Empirically, I will study all games regardless of the outcome and control for the level of risk

taking. However, I also test the sensitivity of the results by comparing the results with games

that ended in draws and that were performed by players that chose a risk-loving opening. I

will also analyze how men and women perform in games shorter and longer than average. In

addition, I compare how they actually score relative to the expected score.

2.4 Self-control problems in chess

Regarding time inconsistency, there are two typical self-control issues in chess. The first is

that some players spend too much time for reflection at each move, to the degree that they

suffer from having to play under time pressure later in the game. The second is that some

players are so eager to move that they tend to move without sufficient reflection and since the

move quality is a function of the reflection time, this may lead to an inefficient time

distribution. Almost a century ago the grandmaster Rudolf Spielmann stated that it is wrong to

search for the best chess move in every position. You should only try to find a sufficiently

good move.9 By searching for the perfect move, you will over-consume the time you have at

your disposal and also risk to exhaust your energy. Webb (2005) writes that:

“…many leading grandmasters are so fascinated by chess that they cannot resist the

challenge of finding the very best move in a position, even if this means spending up to an hour on a

single move. Consequently they often end up having to make their last 10 or 15 moves in less than a

minute.” /:::/ “…[M]any experienced players, including some grandmasters, seem unable to avoid

getting into time-trouble game after game. As a result they regularly throw away good positions and

fail to achieve the results of which they are capable.” (Webb 2005, p. 100-102)

The purpose of introducing a time control limit at the 40th move, is to force a commitment

upon the players to reduce the over-consumption of time. To obtain a measure of potential

time inconsistency in chess, I exploit the existence of the time control limit at the 40th move.

The hypothesis is that those spending more time in the beginning of the game, will score

better in games shorter than average and have a higher propensity to score worse at the 40th

move and in longer games, compared to other moves and players.

9 For an interesting discussion on the rational choice procedure of a chess player, see Simon (1955).

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2.5 Econometric model and control variables

Two econometric models are used to estimate the coefficients of interest. The first is a

regression framework which is estimated with OLS. The dependent variable in the main

model is the number of moves when the game ended. The female dummies are the explanatory

variables of interest. The second model is a difference-in-difference approach where I

compare the performance for men and women at the 40th move time control and with the

moves just before and after the 40th move. The dependent variable is then a ternary variable

which takes on the value 1 if a win, ½ if a draw and 0 if a loss. The model is estimated with

OLS but I also present results with ordered logit for the main model.

Each game counts as one observation. As there are two players in each game I only

include a game once and I randomize which player to be the player in focus. Since a player

usually plays many games in the dataset, I employ standard errors clustered at the individual

level. There are two levels of control variables, game-specific and player-specific. Since the

variable of interest is player-specific (i.e., it is constant over time), it is not possible to hold

constant for individual fixed effects. The player-specific controls are: gender, nationality

(regional dummies) and a female-opponent ratio (share of games played against a female

opponent, see below). The game-specific (time-varying) control variables are: Elo rating

(playing skill), Elo difference, age (age, age squared, age 0–20 years old and age difference),

number of games played (log), piece color (to account for the first-mover advantage),

arranged draws (a draw in less than 20 moves)10, year dummies and risk taking. The data also

include information about the names of the players, the ECO code and the score of the game.

To stimulate women’s participation in chess, there are two types of competitive

events, tournaments for both sexes and tournaments where only women may participate. It is

possible that those women choosing to play in women’s tournaments differ on average from

those playing in mixed-sex tournaments. Since information about the type of tournament is

not available in the dataset, it is not possible to distinguish games played in mixed-sex

tournaments from those played in women’s tournaments. However, in cases when at least one

of the players is a man, we know with certainty that the game was played in a mixed-sex

tournament. As the results are presented for all gender combinations, this should not have any

decisive effect. Moreover, a control for the share of games played against female opposition is

10 Professional players who play chess for a living, sometimes prefer to end a game quickly (by agreeing to an early draw). This is done to save energy and time. When doing this, they typically agree to a draw while the game is still in the theoretical opening phase, hence, in less than twenty moves; see also Moul and Nye (2009) for a discussion.

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included which should capture most of the effect that occurs due to gender differences in the

type of tournament.

3. Data and Statistics

3.1 Descriptive statistics

The main source of information used in this study comes from ChessBase 10, a database

collection with 1.5 million chess games played by expert chess players in international chess

events. It contains more than 30,000 players from 140 countries. I use games played by

players with an Elo rating of at least 2000, above which a player is considered to be an expert

chess player (i.e., either a master or a master candidate). The panel data of this study cover the

years from 1997 to 2007. In addition to the Chessbase data, I have carried out an online

survey at the leading internet chess site, www.chessbase.com, see below.

Table 1 gives the mean duration of the games measured in moves. Column (1)

shows that women´s games last 42.0 moves on average while men´s games last 39.3 moves on

average. Table 1 also gives the mean game duration for two subgroups with different chess

ability and for different game outcomes. Roughly, the group with an Elo rating lower than

2300 are expert amateurs and the higher-rated group with an Elo rating higher than or equal to

2300 are professionals or semi-professionals. For the professionals, the female games last

about four moves longer than the male games, on average. For the amateurs the difference is

smaller, about 2.5 moves.

Table 1 Descriptive statistics for game durations in moves for different subgroups. Duration in moves (1) All players (2) Amateurs, Elo<2300 (3) Professionals Elo>2300

men women men women men women All games, mean 39.31 41.99 38.99 41.55 39.07 42.96 Stand dev (16.77) (16.83) (15.98) (16.34) (17.34) (17.84) Wins, mean 41.48 43.39 41.07 42.99 41.71 44.03 Draws, mean 34.76 39.32 35.61 39.11 34.22 39.68 Losses, mean 41.45 43.08 40.14 42.27 43.40 46.05

Figure 1 displays the pattern around the critical 40th move time control for wins, losses and

draws, and for men and women. It reflects the effect of the time constraint. Although players

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can be short of time also before reaching the 40th move, the effect tends to concentrate at the

40th move.11

Figure 1 a) the number of wins, b) the number of losses, c) the number of draws. The number of male games has been divided by 10.

600

800

1000

1200

1400

1600

1800

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

men women

600

800

1000

1200

1400

1600

1800

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

men women

a) No. of wins at each game length (in moves) b) No. of losses at each game length (in moves)

600

800

1000

1200

1400

1600

1800

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

men women

c) No. of draws at each game length (in moves)

3.2 The survey data

To obtain additional data on time preferences and time inconsistency, a survey was carried

out among expert chess players. A questionnaire was posted at the world’s leading internet

chess site, www.chessbase.com. The survey was run between the 30th of September and the

4th of October in 2011 and obtained 1,620 respondents. The questionnaire contained five

questions where the respondents could rate between zero and ten, and one question where

they answered whether they were smokers or not (yes or no). In addition, they were asked to 11 Some of the effect is expected to spill over to the 41st period as it is not uncommon that the last moves before the time control are played so quickly that the player in time trouble does not have time to properly evaluate the position. Once the time control is passed, the player realizes that the position is lost (given that it is) and resigns. For this reason, some of the games won/lost when playing under time pressure are registered as won/lost in period 41.

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give their names and email address. A lottery prize of 500 USD as a value check at

www.amazon.com was given to a winner. By using the names of the players participating in

the survey, it was possible to match 235 players out of the 1,620 respondents to the

ChessBase dataset used in this paper.12

The questions asked in the survey are given in Table 2 and concern impatience in

chess, performance under time pressure in chess, patience in general, risk in general and

whether the player smokes regularly. Table 2 also gives the Spearman correlation between

any two questions with the significance, p-values, in brackets.

Table 2 Spearman correlation matrix between the answers of the survey questions. Ratings between 0 and 10, smoking either 0 or 1(smoker). Do you consider

yourself an impatient player when playing a

chess game?(0=not at

all, 10=very much)

Do you think you would perform better in chess if you could avoid time pressure? (0=not at all, 10=very much)

Do you think you tend to be too impatient when playing chess? (0=not at all, 10=very much)

Do you smoke regularly? (yes/no)

In life in general, do you consider yourself a patient person or do you consider yourself to be impatient? (0=very impatient, 10=very patient)

Do you think you would perform better in chess if you could avoid time pressure? (0=not at all, 10=very much)

-0.0873

(0.0005)

Do you think you tend to be too impatient when playing chess? (0=not at all, 10=very much)

0.8016

(0.0000)

-0.0294 (0.2404)

Do you smoke regularly? (yes or no)

0.0857

(0.0006)

-0.0128 (0.6116)

0.0859 (0.0006)

In life in general, do you consider yourself a patient person or do you consider yourself to be impatient? (0=very impatient, 10=very patient)

-0.2267 (0.0000)

0.0862 (0.0005)

-0.2267 (0.0000)

-0.0664 (0.0080)

In life in general, are you fully prepared to take risks or do you try to avoid risks? (0=minimum risk, 10=maximum risk)

0.0972 (0.0001)

-0.0207 (0.4071)

0.0644 (0.0099)

0.0309 (0.2182)

-0.0249 ( 0.3182)

12 The survey participants were required to have at least an Elo of 2000. The reason for not finding more matches is because a substantial part of the players have improved between 2007 and 2011. Since the survey was carried out in 2011, and the ChessBase data end in 2007, some players who had an Elo of at least 2000 in 2011, had an Elo below 2000 in 2007. Also, some players have spelled their names slightly different (using short names, dropping initials etc) and the ChessBase requires an exact match. Some players may also be missing in the data.

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As Table 2 shows, the players interpret impatient and too impatient as basically the same

question (the correlation is .8 and highly significant), which indicates that impatience is a

rather negative attribute in chess. Since these two answers correlate so highly, I will address

only impatient in the remainder of the paper. Moreover, impatience in chess is negatively

correlated with performing better without time pressure, positively correlated with being a

smoker, negatively correlated with patience in life in general, and positively correlated with

being risk-loving in life in general. In addition, performing better without time pressure is

positively correlated with patience in life in general. Thus, the questions are correlated as

expected. The rater characteristics and survey statistics are to be found in Tables A.1 and A.2

in the Appendix.

4. Results

In column (1) of Table 3, I present the coefficients when all games are included. We see that

the coefficients of interest, opposite-sex players and both are female players, are significantly

positive. Opposite-sex players play about .3 moves longer games than two males. Two female

players play about 2.1 moves longer games than two males. Column (2) and (3) give the

results for amateur and professional players, respectively. The gender difference for

professionals is larger than for amateurs. Column (4) shows the coefficients when only

including drawn games in the regression. The gender difference remains and is about 1.1

moves for two women and about .5 moves for opposite-sex players compared to two men.

The conclusion is that women tend to increase the game duration in moves and since games

played by two women are even longer than mixed-sex games, this is not likely to be due to a

change in the male behavior (due to the opponent being a woman) but is rather a female

preference.

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Table 3 Game duration in moves regressed with OLS on opposite-sex players and both are female players, where the comparison group is both are male players. Dep var: game length in moves All players

and games Amateurs Elo<2300

Professionals Elo>2300

Including only draws13

(1) (2) (3) (4) Opposite-sex players .2948 .1113 .5606 .5144 (.1182)** (.1309) (.2255)** (.2050)** Both are female players 2.1311 1.6008 2.8093 1.0729 (.2240)*** (.2534)*** (.4291)*** (.3962)** Elo .0035 .0044 .0032 -.0011 (.0003)*** (.0004)*** (.0006)*** (.0004)** Elo difference -.0025 .0003 -.0058 .0001 (.0002)*** (.0002)* (.0002)*** (.0003) Age -.0582 -.0084 -.0931 -.0414 (.0130)*** (.0151) (.0231) *** (.0192)** Age-squared .0006 .0002 .0007 .0001 (.0001)*** (.0002) (.0003)*** (.0002) Teenage -.0197 .0403 .0186 .0901 (.0966) (.1223) (.1439) (.1512) Age difference .0057 -.0086 .0244 .0177 (.0014)*** (.0019)*** (.0021)*** (.0024)*** Arranged draws14 -28.9749 -28.3357 -29.5044 -28.9678 (.0482)*** (.0545)*** (.0699)*** (.0742)*** White pieces (1st mover adv.) .0023 .2598 -.2235 -.0234 (.0349) (.0503)*** (.0491)*** (.0592) Share of female opponents, .3322 .1539 .2713 .8877 player (.1924)* (.2140) (.4150) (.3471) Share of female opponents, .3744 .7224 .2619 .4858 opponent (.1815)** (.2154)** (.3378) (.3281) Number of games (log) .2360 .4014 .0780 .1202 (.0339)*** (.0378)*** (.0595) (.0531)** Risk-loving player15 -.6622 -.7444 -.6062 -.0690 (.0461)*** (.0633)*** (.0643)*** (.0790) Risk-loving opponent -.5773 -.6226 -.5358 .0072 (.0443)*** (.0622)*** (.0632)*** (.0770) Constant 33.5613 30.5672 36.1150 45.2535 (.6192)*** (.9363)*** (1.3459)*** (.9219)*** Regional dummies, both pl. Yes Yes Yes Yes Year dummies Yes Yes Yes Yes R-squared .247 .202 .283 .423 Number of players 32,148 28,548 7,302 25,257 Number of observations 738,989 340,132 396,917 269,773 Notes: Western Europe is used as the comparison group for the regional dummies. Robust standard errors in parentheses, clustered at player level. *** significant at 1%, ** significant at 5%, * significant at 10%.

The results in Table 3, show that women play longer games than men on average. Since I

include controls for risk taking in the opening, these differences are not likely to arise due to

differences in risk preferences. Moreover, since women have been found to be more risk- 13 Conditioning on both players being risk-loving (choosing risky openings) and the result being a draw produces similar results as in column (4). 14 Excluding the control for arranged draws, increases the gender differences. Male players are more prone to accept arranged draws, also when controlling for Elo, Elo difference, number of games played etc, which is interesting per se. 15 Risk-loving is a dummy variable taking on the value one if risk-loving, zero otherwise (including neutral or risk-averse).

15

averse, see Gerdes and Gränsmark (2010), the risk taking effect is likely to affect the results

in the opposite direction, i.e., women should play shorter games on average. This is

particularly true for draws since accepting a draw rather than playing for a win with the risk of

losing is a risk-averse behavior. Later in this section, I also include a second risk control

based on a player´s self-reported risk taking in real life.16

To establish how the gender differences in game duration affect performance, Table 4

presents the results when the Elo difference between two players is regressed on the female

dummies, when conditioning on the game outcome being a draw. Thus, column (1) of Table 4

tells us how women perform, relative to men, when agreeing to draws, compared to the

expected score. By conditioning on a draw, we know that the actual performance was .5. An

Elo difference of +30 corresponds to approximately +8 percentage points difference, i.e. .54

vs. .46 in expected score. To accept .5 when your expected score is .54 can be seen as the

player being willing to pay a price to achieve a draw in the present period rather than

continuing the game with an expected score of .54, given that we can hold constant for risk-

aversion. We see that when the player in focus is a woman playing against a man, the Elo

difference is negative compared to the comparison group (man vs. man), indicating that, on

average, women perform better than their expected score (which is smaller than .5 since the

Elo difference is negative). A coefficient of -11 should be interpreted as the expected score

being roughly .485. When a man plays against a female opponent, the Elo difference is 30

points larger than for the comparison group (man vs. man), meaning that the expected score is

roughly .54. Thus, the conclusion from Table 4 is that men are willing to pay a higher price

than women to end the game sooner when playing against a woman. Note that any given

game where the players agree to a draw would have been ended later had they not agreed to a

draw.

16 The differences could arise from a potential gender difference in the intensity of tournament participation (playing many games might affect how long games you want to play), but there is no significant gender difference in intensity and I also control for the number of games played.

16

Table 4 Elo difference (cost) for ending the game, conditional on the outcome being a draw. The Elo difference is defined as Elo (player) – Elo (opponent). Dep. Var. Elo diff. conditional on result=draw Draw=1 Stand. error (1) (2) Female vs. male opponent -11.2090 (3.2972)*** Male vs. female opponent 30.9286 (2.1230)*** Female vs. female opponent -21.2569 (2.7769)*** Elo .3660 (.0051)*** Age -.2659 (.2117) Age-squared .0086 (.0025 )*** Teenage -.7143 (1.4548) Age difference .5360 (.0240)*** Share of female opponents, player -5.2281 (3.9907) Share of female opponents, opponent 89.7461 (3.2035)*** Number of games (log) -10.6175 (.5093)*** Risk-loving player -.0618 (.6230) Risk-loving opponent 6.8732 (.5946)*** White pieces (first-mover adv.) -20.7119 (.4291)*** Constant -808.8361 (10.0483)*** Year and regional dummy Yes R-squared .214 Number of players/observations 25,336 / 269,773 Notes: Western Europe is used as the comparison group for the regional dummies. Robust standard errors in parentheses, clustered at player level. *** significant at 1%, ** significant at 5%, * significant at 10%. A potential explanation for these findings is that men have a lower discount factor and want to

end the game sooner. Another explanation could be that men spend less time in the beginning

of the game and fail to achieve the position they have the capacity of, with the consequence

that they tend to accept a draw against an inferior opponent more often.

In Table 5, I turn to the survey subsample. From column (1), we see that players who

have reported that they are impatient in chess play significantly shorter games, about .9 moves

shorter games. The magnitude of the coefficient is obtained by multiplying the mean rating

for impatience which is 3.55, see Table A2 in Appendix, with the coefficient .237 in Column

(1). Players who smoke play significantly shorter games, about 1.1 moves, see column (2).

Players who have reported that they are patient in life in general, play about .6 moves longer

games (6.4*.10), although this coefficient is not significantly different from zero. Note that

the number of players in this subsample is substantially lower which produces larger standard

errors. As an extra control I also include risk-taking in life in general.

17

Table 5 Survey data. Game duration in moves regressed with OLS on impatience in chess, being a smoker and patience in life in general.17 Dep var: game length in moves Impatience Smoker Patience in general (1) (2) (3) Impatience in chess (0-10) -.2373 - - (.0766)*** Smoker (0 or 1) - -1.1331 - (.6565)* Patience in general (0-10) - - .1005 (.0775) Risk-loving in general (0-10) -.0816 -.0199 -.0764 (.0784) (.0873) (.0769) The same controls as in Table 3 … … … R-squared .207 .207 .206 Number of players/observations 231 / 18,224 230 / 18,214 230 / 18,208 Notes: Western Europe is used as the comparison group for the regional dummies. Robust standard errors in parentheses, clustered at player level. *** significant at 1%, ** significant at 5%, * significant at 10%. If women prefer to use more time in the beginning of the game, resulting in a higher initial

move quality, then they are likely to have to settle with a lower move quality later in the game

(due to the time constraint). In Table 6, I regress the game result on a short-game/long-game

dummy (1 if less or equal to 38 moves, zero if more than 38). The median game duration in

moves is 38, and due to the right-skewed distribution (one is the lower limit but there is no

upper limit), I choose the median as a cut-off value rather than the mean.18 In the four

columns of Table 6, I regress on four different variables, female, impatience, patience in

general and performance without time pressure. As the regression is a difference-in-

difference approach, the variables of interest are the interaction coefficients. These

coefficients reveal whether the player in focus (indicated by A/B/C/D, where each letter

denotes one of the studied groups) performs better in shorter games compared to longer

games and compared to the comparison group. We see that women (A) perform comparably,

and significantly, better in games lasting less than or equal to 38 moves compared with longer

games and the comparison group (male players). Impatient players (B), in column (2), are

expected to play (too) quickly in the beginning of the game and, hence, score worse in shorter

games compared to longer. This pattern is confirmed by the empirical findings as the

coefficient is highly significant. In column (3) and (4), I find weak support for patience in

general (C) and performance without time pressure (D) leading to better performance in

shorter games. However, although these coefficients have the expected sign, they are far from 17 It would have been interesting to compare how men and women answered the survey questions. Unfortunately, only eleven players were identified as females which is not sufficient to be used for inference. 18 However, the results in Table 6 are not sensitive to either the mean, median or other close values as 30, 35 or 40. Neither does a dummy denoting 1-39 and 42-upwards, excluding the critical 40th and 41st move, affect the findings more than marginally.

18

significant. These findings give support to the hypothesis that impatient players perform

worse in the beginning of a game.

Table 6 Performance for four different categories for games shorter than 38 and longer or equal to 38 moves, estimated with a diff-in-diff. model (=1 if 1-37, =0 otherwise). Dep. var. Result A.. Female B. Impatience C. Patience in gen D. No time pressure (1) (2) (3) (4) Move dummy (1-37) -.0007 .0249 -.0178 -.0234 (.0009) (.0122)*** (.0178) (.0146) A/B/C/D -.0378 .0015 -.0001 -.0027 (.0036)*** (.0022) (.0022) (.0016) Move dummy * A/B/C/D .0082 -.0078 .0015 .0024 (.0030)*** (.0026)*** (.0026) (.0027) Control var. as in Table 3

If women spend more time in the first 38 moves, they are more likely to fall short of time

(and move quality) later in the game, in particular when approaching the 40th move time

control. In Table 7, I present the coefficients for a difference-in-difference (or, rather, a triple-

diff.) regression. Games ended in 35 to 45 moves are included, where move 40 is the critical

point. Players in time pressure are expected to perform worse at the 40th move compared to

other game lengths (35 to 45) and compared to the comparison group. The dependent variable

is the result of the game (i.e., performance). The variable of interest is the Female * 40th move

coefficient. (not the Female * Female opponent * 40th move, since two women are not

expected to perform differently than two men). Column (1) gives the result for the whole

population and it shows that women perform 2.9 percent worse in the 40th move. Column (2)

and (3) reveal that this finding originates from gender differences at the amateur level. There

is no significant gender difference for professional players. Column (4) strengthens the

credibility of the results as a similar pattern is found when estimating with an ordered logit

model. The conclusion from Table 7 is that women perform worse than men at the critical 40th

move time control. This is consistent with the hypothesis that women spend more time in the

beginning and are more likely to be short of time later in the game.

19

Table 7 Performance at the critical 40th move with female dummies. The dep. var. is either 1, ½ or 0 (win, draw or loss). The model is estimated by OLS in a diff-in-diff. approach where the 40th move dummy is 1 if move 40, zero if move 35-39 or 41-45.19

Dep. var. Results (1, ½, 0) ,for moves 35-45

All players, OLS

Amateurs, Elo<2300, OLS

Professionals, Elo>2300, OLS

All players Ordered Logit

(1) (2) (3) (4) Female -.0340 -.0447 -.0071 -.1782 (.0069)*** (.0079)*** (.0141) (.0376)*** 40th move -.0013 -.0061 .0029 -.0091 (.0029) (.0045) (.0039) (.0157) Female opponent .0157 .0168 .0087 .0876 (.0064)** (.0089)* (.0092) (.0345)** Female * 40th move -.0286 -.0482 .0147 -.1489 (.0138)** (.0173)*** (.0234) (.0773)* Female opponent * 40th move -.0112 -.0270 .0071 -.0497 (.0149) (.0226) (.0196) (.0829) Female * female opponent .0035 .0018 .0193 .0211 (.0080) (.0106) (.0128) (.0433) Female * female opp. * 40th .0618 .0964 .0126 .3000

move (.0228)*** (.0307)*** (.0384) (.1252)** White pieces .0857 .0699 .0995 .4441 (.0017)*** (.0025)*** (.0022)*** (.0090)*** Elo -.0002 -.0002 -.0001 (-.0010) (.00001)*** (.00002)*** (.00002)*** (.00005) Elo difference20 .0012 .0012 .0013 .0067 (0.0001)*** (0.0001)*** (0.0001)*** (.00004) Age .0009 -.0006 .0019 .0063 (.0005)* (.0006) (.0007)*** (.0025)** Age squared -0.0001 0.0001 -.00001 -.00005 (0.0001) (0.0001) (0.0001) (.00003)* Age difference -.0023 -.0023 -.0022 -.0125 (.0001)*** (.0001)*** (.0001)*** (.0004)*** Teenager <20 years old .0131 .0013 .0192 .0790 (.0036)*** (.0054) (.0050)*** (.0189)*** Risk-loving player -.0022 -.0010 -.0033 -.0120 (.0021) (.0031) (.0028) (.0111) Risk-loving opponent .0023 .0049 0.0001 .0134 (.0021) (.0031) (.0028) (.0111) Share of female opponents, -.0250 -.0050 -.0843 -.1367

player (.0095)*** (.0104) (.0221)*** (.0514)*** Share of female opponents, .0181 .0064 .0322 .0964

opponent (.0089)** (.0117) (.0135)** (.0484)** number of games (log) .0312 .0330 .0274 .1668

(.0011)*** (.0015)*** (.0018)*** (.0063)*** Constant .7190 .8598 .5824 - (.0228)*** (.0421)*** (.0395)*** R squared .236 .195 .227 .126 Number of players/games 25,633/203,673 22,006/95,539 6,438/107,579 25,633/203,673

Notes: Western Europe is used as the comparison group for the regional dummies. Robust standard errors in parentheses, clustered at player level. * significant at 10%; ** significant at 5%; *** significant at 1%

19 Without the move restriction of games ended in 35 to 45 moves, i.e., when all games are included, the coefficient of interest is -.03001 (.0135)***. 20 The Elo difference is highly correlated with the result. However, removing the variable Elo difference from the regressions only affects the results marginally.

20

In Table 8, I return to the survey subsample where I focus on patience in general, performance

without time pressure, smokers and impatience in chess. The variables of interest are the

coefficients of the interaction term. In line with the hypothesis and earlier results of this study,

we see that players who are patient in life in general tend to end up in time pressure (perform

worse) at the critical 40th move, compared to other moves and groups. Multiplied by the mean

rating, see Table A.2 in Appendix, I obtain a magnitude of about 7.5 percent lower

performance at the 40th move. The coefficient is significantly different from zero. A similar

pattern is found for performance without time pressure although the coefficient is smaller and

insignificant. The results in column (3) suggest that smokers perform 8.3 percent better at the

40th move. The result for impatience in chess is approximately zero and insignificant.

Table 8 Survey data. Performance at the 40th move and for patience in general, performance without time pressure, smoker and impatience. The model is estimated by OLS in a diff-in-diff. approach where the 40th move dummy is 1 if move 40, zero if move 35-39 or 41-45.21 Dep var: Result (1, ½, 0) Patience No time pres. Smoker Impatience (1) (2) (3) (4) 40th move .088649 .0618 -.0025 .0180 (.0410)** (.0350)* (.0231) (.0322) Patience in general .0023 - - - (.0028) Performance without time - -.0025 - -

pressure (hypothetically) (.0020) Smoker - - .0032 - (.0147) Impatience in chess - - - .0032 (.0027) Patience in gen * 40th move -.0130 - - - (.0064)** Performance without time - -.0085 - -

pressure * 40th move (.0061) Smoker * 40th moves - - .0830 - (.0306)*** Impatience * 40th move - - - .0006 (.0075) Risk-loving in general -.0004 .0001 -.0010 -.0002 (.0027) (.0026) (.0029) (.0026) Controls as in Table 3 … … … … R-squared .250 .244 .244 .244 Number of players/obs. 210 / 5,115 211 / 5,118 210 / 5,115 211 / 5,118

21 The corresponding coefficients of the variables of interest estimated by ordered logit are similar. The coefficients are:: smoker*40th move: .4251 (.1669)**, no-time-pressure*40th move: -.0421 (.0329), impatience*40th move: .0015 (.0394) and patience in general*40th move: -.0802 (.0360)**.

21

5. Conclusion

This paper finds that male players play shorter games than their female peers on average, and

that they are willing to pay a price in the shape of reduced performance to shorten the game.

As a consequence, female players perform relatively better in the beginning of the game while

male players perform better in the second half. Moreover, women perform worse than men at

the 40th move time control. A plausible interpretation is that women spend more time in the

beginning of the game and thereby obtain a higher move quality in the beginning. In the

second half women are forced, to a higher extent than men, to play with less time for

reflection due to the time constraint.

The complementary small-scale survey shows that impatient players play shorter

games. The fact that the questions about impatience and being-too-impatient correlate so

highly, suggests that this behavior is partly inconsistent. The fact that the data is self-reported

indicates that the players are aware of the behavior. This implies that they tend to make a

move faster than they would like to do in the long run. Smokers show a similar behavior and

since smoking is a notorious example of inconsistency, it seems reasonable to interpret this as

a self-control problem. Furthermore, the fact that patient players and players who reported

that they would perform better without time pressure, actually perform worse at the 40th

move, gives further support to the interpretation.

In economic terms, the findings suggest that male players are more impatient than

female players. As to potential self-control problems, men are more inconsistent in the sense

that they tend to be too impulsive whereas women are inconsistent in the sense that they tend

to over-consume reflection time. It is possible that women are more indecisive and strive for

perfectionism to a larger extent than male players. Nevertheless, given that you are aware of

the indecisiveness or perfectionism, this is still a self-control problem.

Alternative explanations to the results could be that men and women differ in their

perception of effort or that they have different planning abilities or degree of awareness. In

psychological research, women, not men, are generally found to be better at planning, see for

instance Naglieri and Rojahn (2001) and references given therein. Whatever the underlying

explanation to the findings, there is a gender difference which may be important to help us

understand gender differences and interactions in daily life.22

22 Furthermore, the fact that the gender differences survive nationality controls makes it tempting to conclude that the behavior is universal. However, this does not necessarily mean that the difference is genetic, see, for example, Lundborg and Stenberg (2010) for a discussion.

22

One objection that could be raised against this study is that it focuses on a non-

representative selection of people. For this reason we should be careful not to generalize the

results too far. Nonetheless, in light of the opinion that expert chess players are highly rational

and act in a highly competitive environment, we would expect their behavior to be a lower

bound as regards gender differences in impatience and self-control problems. The

accumulated picture of the results is that the magnitude of the gender difference in impatience

and inconsistency is about 2 to 5 percent. However, since we do not know with certainty

whether these findings really constitute a lower bound or not, some measure of cautiousness

when interpreting the results is called for. It is also possible that the data suffer from sample

selection, not least because the female share is about 10 percent.

There are particularly three aspects that could be highlighted in future research on this

topic and data. Thanks to the panel structure of the data it is possible to follow a player over

time to study the development of the inconsistent behavior as a player develops in playing

skill. A player that improves in self-control would be expected to improve in Elo rating. It

would also be possible to construct a quasi-experiment by exploiting the so called Fischer

time (possible with digital clocks). With Fischer time a player receives an additional 30

seconds (usually) for every move and therefore the 40th move time constraint is substantially

relaxed in practical play. By comparing the gender differences in tournaments played with

and without Fischer time it should be possible to create a reasonably counter-factual control

group. Finally, with the increasing popularity of online chess tournaments on the Internet, it

should be possible to collect data on the exact amount of time spent on each single move.

That could give rise to some interesting further research which would be more precise than in

the present study.

References

Akerlof, G., 1991, Procrastination and Obedience, American Economic Review, 81, pp. 1–19.

Angeletos, G. M., Laibson, D., Repetto, A., Tobacman, J., Weinberg, S., 2001, The

Hyperbolic Consumption Model: Calibration, Simulation and Empirical Evaluation,

Journal of Economic Perspectives, 15, pp. 47–68.

Ariely, D., Wertenbroch, K., 2002, Procrastination, Deadlines, and Performance: Self-control

by Precommitment. Psychological Science, Vol. 13, No. 3: 219-224.

Ashraf, N., Karlan, D., Yin, W., 2006, Tying Odysseus to the Mast: Evidence

from a Commitment Savings Product in the Philippines, Quarterly Journal of

Economics, 121, pp. 635–672.

23

Benzion, U., Shachmurove, Y., Yagil, J., 2004, Subjective Discount Functions –

An Experimental Approach,” Applied Financial Economics, 14, pp. 299–311.

Chabris, C., Glickman, M., 2006, Sex Differences in Intellectual Performance – Analysis of a

Large Cohort of Competitive Chess Players, Psychological Science, 17, pp. 1040–1046.

Croson, R., Gneezy, U., 2009, Gender Differences in Preferences. Journal of Economic

Literature, 47, pp. 448–474.

DellaVigna, S., Paserman, D., 2005, Job Search and Impatience, Journal of Labour

Economics, 23.

Elo, A., 1978, The Rating of Chess Players, Past and Present, (London: Batsford).

Fischer, C., 1999, Read this paper later, Journal of Economic Behavior and Organization, 46,

pp. 249–269.

Gerdes, C., Gränsmark, P., 2010, Strategic Behavior Across Gender: A Comparison of

Female and Male Expert Chess Players, Labour Economics.

Gobet, F., 2005, Chunking Models of Expertise: Implications for Education, Applied

Cognitive Psychology, 14, pp. 183–204.

Harison, G., Lau, M., Williams, M., 2002, Estimating Individual Discount Rates in Denmark:

A Field Experiment, American Economic Review, 92, pp. 1600–1617.

Laibson, D., 1997, Golden eggs and Hyperbolic Discounting, Quarterly Journal of

Economics, 112, pp. 443–477.

Levitt, S., List, J., Sadoff, S., 2009, Checkmate: Exploring Backward Induction

Among Chess Players, NBER Working Paper Series,

http://www.nber.org/papers/w15610

Lundborg, P., Stenberg, A., 2010, Nature, Nurture and Socioeconomic Policy – What Can We

Learn from Molecular Genetics? Economics and Human Biology 8, pp. 320-330.

Moul, C., Nye, J., 2009, Did the Soviets Collude? A Statistical Analysis of Championship

Chess 1940–1978, Journal of Economic Behavior & Organization, 70, pp. 10–21.

Naglieri, J., Rojahn, J., 2001, Gender Differences in Planning, Attention, Simultaneous, and

Successive (PASS) Cognitive Processes and Achievement, Journal of Educational

Psychology, 93, pp. 430-437.

O’Donoghue, T., Rabin, M., 1999, Doing It Now or Later, American Economic

Review, 89, pp. 103–124.

Palacios-Huerta, I., Volij, O., 2009, Field Centipedes, American Economic Review, 99,

pp.1019-1035.

24

Phelps, E. S., Pollack, R. A., 1968, On Second-Best National Saving and Game-Equilibrium

Growth, Review of Economic Studies, 35, pp. 185–199.

Pollack, R. A., 1968, Consistent Planning, Review of Economic Studies, 35,

pp. 201–208.

Roring, R., 2008, Reviewing expert chess performance: a production based theory of chess

skill, Dissertation, Department of Psychology, Florida State University.

Ross, P., 2006, The Expert Mind, Scientific American, 295, pp. 64–71.

Shahade, J., 2005, Chess Bitch: Women in the Ultimate Intellectual Sport, (Los Angeles,

USA: Siles Press).

Simon, H., 1955, A Behavioral Model of Rational Choice, Quarterly Journal of

Economics, 69, pp. 99–118 .

Strotz, R. H., 1956, Myopia and Inconsistency in Dynamic Utility Maximization, Review of

Economic Studies, 23, pp. 165–180.

van Harreveld, F., Wagenmakers, E. J., van der Maas, H., 2007, The effects of time pressure

on chess skill: an investigation into fast and slow processes underlying expert

performance, Psychological Research, 71, pp. 591–597

Webb, S., 2005, Chess for Tigers, 3rd ed., (London: Batsford).

Appendix

Table A.1 Rater characteristics

Rater characteristics

Smoker No: 198 (85%) Yes: 35 (15%)

Mean Elo 2167.047 St. dev. 128.709

Mean age 36 (in 2011) St. dev. 12.337

Gender Male: 224 (95.2%) Female: 11 (4.8 %)

25

Table A.2 Survey statistics

Survey characteristics

Impatient, 0=not at all,

10=very much

Patient in gen., 0=very

imp., 10=very pat.

Risky in gen., 0=min

risk, 10=max risk

No time pressure, 0=not

at all, 10=very much

No. of players 234 233 233 234

Mean rating 3.555 (2.520) 6.377 (2.479) 4.519 (2.515) 5.948 (3.152)

rate answers % answers % answers % answers %

0 27 11.54 1 0.43 8 3.43 15 6.41

1 25 10.68 5 2.15 17 7.30 7 2.99

2 39 16.67 16 6.87 34 14.59 25 10.68

3 45 19.23 19 8.15 42 18.03 25 10.68

4 18 7.69 17 7.30 16 6.87 4 1.71

5 27 11.54 22 9.44 30 12.88 19 8.12

6 15 6.41 17 7.30 21 9.01 12 5.13

7 15 6.41 39 16.74 34 14.59 28 11.97

8 18 7.69 54 23.18 21 9.01 46 19.66

9 2 0.85 23 9.87 4 1.72 17 7.26

10 3 1.28 20 8.58 6 2.58 36 15.38